25 
to render difficult, to some minds, the right apprehension of 
its action in regard to 'dhe motion of the vessel, it will he 
necessary to consider here two ships being propelled by 
a screw propeller, placed in two hypothetical positions 
as follows. 
Ship A. This ship is propelled by a screw revolving in a 
position astern, that is, out of the wake of the ship in still 
water. 
Ship B. This ship is propelled by a screw revolving in a 
position astern, that is, in the wake of the ship in water 
which flows in the direction of the ship with a velocity Y. 
With respect to the ship A, the slip of the element {a) is 
computed on the above principal in Arts. 12 and 13, and is 
correctly represented by the formula 
H'-H = 27t| l (13) 
( COSa u j 
with a screw revolving as above described there would be, 
indeed, just ground for surprise if (H' — H) was experi- 
mentally observed to be either a negative quantity, or zero 
16. With respect to the ship B. Put u', v'for the angular 
velocity, the velocity of the element (a) in the direction of 
the axis, repectively, in order to produce the normal velocity 
equal to zero. 
The slip will he here computed by the element {a) moving 
in such a manner that its normal velocity is zero. 
Now, having regard to Y, there results from formula (4) 
Art. 6, the equation 
Tu'cOBv - {v' - Y)cosa = 0. 
(14) 
. V Y TCO^V 
r rom which, — , = — ; -l , 
' u u COSa 
Next to find the distance H' traversed along the axis AB 
during one revolution of the element (a) of the propeller 
blade — 
Time of one revolution = 
space 
velocity 
.STT 
u' 
.*. H' = time x velocity = = 27 t -f — , + 1 (15) 
u I u COSa ) 
